##### Department of Mathematics,

University of California San Diego

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### Number Theory

## Sug Woo Shin

#### MIT

## Patching and the p-adic Langlands correspondence

##### Abstract:

This is a report on joint work with Ana Caraiani, Matthew Emerton, Toby Gee, David Geraghty, and Vytautas Paskunas. We will explain some ideas around the global construction of new representation-theoretic objects called "patched modules" by a variant of the Taylor-Wiles-Kisin method. They are in many ways better suited than p-adically completed cohomology for a global attempt to understand the p-adic local Langlands correspondence. As an application, we obtain new cases of the Breuil-Schneider conjecture.

Host: Claus Sorensen

### December 5, 2013

### 12:00 PM

### AP&M 7321

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